diff --git a/.github/workflows/tests.yaml b/.github/workflows/tests.yaml
index 3295172dd51..7eebbb6aef2 100644
--- a/.github/workflows/tests.yaml
+++ b/.github/workflows/tests.yaml
@@ -203,7 +203,7 @@ jobs:
           set -o pipefail
           mkdir reports
 
-          pytest distributed \
+          pytest distributed/deploy/tests/test_spec_cluster.py \  # DNM
             -m "not avoid_ci and ${{ matrix.partition }}" --runslow \
             --leaks=fds,processes,threads \
             --junitxml reports/pytest.xml -o junit_suite_name=$TEST_ID \
diff --git a/distributed/deploy/spec.py b/distributed/deploy/spec.py
index de48a231ad4..619d73c01fa 100644
--- a/distributed/deploy/spec.py
+++ b/distributed/deploy/spec.py
@@ -379,13 +379,17 @@ async def _correct_state_internal(self) -> None:
                 self._created.add(worker)
                 workers.append(worker)
             if workers:
-                await asyncio.wait(
-                    [asyncio.create_task(_wrap_awaitable(w)) for w in workers]
-                )
+                worker_futs = [asyncio.ensure_future(w) for w in workers]
+                await asyncio.wait(worker_futs)
+                self.workers.update(dict(zip(to_open, workers)))
                 for w in workers:
                     w._cluster = weakref.ref(self)
+                # Collect exceptions from failed workers. This must happen after all
+                # *other* workers have finished initialising, so that we can have a
+                # proper teardown.
+                await asyncio.gather(*worker_futs)
+                for w in workers:
                     await w  # for tornado gen.coroutine support
-            self.workers.update(dict(zip(to_open, workers)))
 
     def _update_worker_status(self, op, msg):
         if op == "remove":
@@ -467,10 +471,14 @@ async def _close(self):
         await super()._close()
 
     async def __aenter__(self):
-        await self
-        await self._correct_state()
-        assert self.status == Status.running
-        return self
+        try:
+            await self
+            await self._correct_state()
+            assert self.status == Status.running
+            return self
+        except Exception:
+            await self.close()
+            raise
 
     def _threads_per_worker(self) -> int:
         """Return the number of threads per worker for new workers"""
diff --git a/distributed/deploy/tests/test_spec_cluster.py b/distributed/deploy/tests/test_spec_cluster.py
index f875db0c3ed..8f6550cc4d0 100644
--- a/distributed/deploy/tests/test_spec_cluster.py
+++ b/distributed/deploy/tests/test_spec_cluster.py
@@ -207,7 +207,7 @@ async def test_restart():
                 await asyncio.sleep(0.01)
 
 
-@pytest.mark.skipif(WINDOWS, reason="HTTP Server doesn't close out")
+@pytest.mark.repeat(50)  # DNM
 @gen_test()
 async def test_broken_worker():
     class BrokenWorkerException(Exception):
@@ -216,7 +216,6 @@ class BrokenWorkerException(Exception):
     class BrokenWorker(Worker):
         def __await__(self):
             async def _():
-                self.status = Status.closed
                 raise BrokenWorkerException("Worker Broken")
 
             return _().__await__()
@@ -226,13 +225,9 @@ async def _():
         workers={"good": {"cls": Worker}, "bad": {"cls": BrokenWorker}},
         scheduler=scheduler,
     )
-    try:
-        with pytest.raises(BrokenWorkerException, match=r"Worker Broken"):
-            async with cluster:
-                pass
-    finally:
-        # FIXME: SpecCluster leaks if SpecCluster.__aenter__ raises
-        await cluster.close()
+    with pytest.raises(BrokenWorkerException, match=r"Worker Broken"):
+        async with cluster:
+            pass
 
 
 @pytest.mark.skipif(WINDOWS, reason="HTTP Server doesn't close out")